Norwich City forward Teemu Pukki scored twice in Helsinki and Jasse Tuominen also netted to bring the home crowd pouring onto the pitch at the final whistle as Finland secured second place behind Group J winners Italy.
Armenia's 1-0 defeat at home to Greece was immaterial as Finland made their finals berth safe with 18 points, seven ahead of the Greeks with a game left to play.
Pukki's goalscoring form in the Premier League has dried up but he was sharp from the first whistle in the Finnish capital.
When his surge for goal was stopped by a Liechtenstein challenge the ball fell into the path of Tuominen who slid home in the 21st minute to open the scoring.
Liechtenstein held firm until half-time but in the 64th minute Pyry Soiri was felled by Livio Meier and Pukki calmly sent goalkeeper Benjamin Buechel the wrong way from the penalty spot.
Pukki got his second goal after rounding the 'keeper only to see his shot stopped on the line, but he reacted quickest to lash in the rebound.